minimum of a function
In the following roblem,
find the least value of the function:
f(x)= +|x-a| +|x-b| + |x-c|
where x is real and, a<B<C< real fixed are a,b,c,d>
i tried using the AM-GM inequality but it was of no use. how should i start?
Notice that f(x) is the sum of three non-negative functions |x-a|, |x-b|, |x-c| having minimums at a,b,c respectively.